Solve for $x$ and $y$ using elimination. ${6x+4y = 88}$ ${-5x+3y = -29}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-3$ and the bottom equation by $4$ ${-18x-12y = -264}$ $-20x+12y = -116$ Add the top and bottom equations together. $-38x = -380$ $\dfrac{-38x}{{-38}} = \dfrac{-380}{{-38}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {6x+4y = 88}\thinspace$ to find $y$ ${6}{(10)}{ + 4y = 88}$ $60+4y = 88$ $60{-60} + 4y = 88{-60}$ $4y = 28$ $\dfrac{4y}{{4}} = \dfrac{28}{{4}}$ ${y = 7}$ You can also plug ${x = 10}$ into $\thinspace {-5x+3y = -29}\thinspace$ and get the same answer for $y$ : ${-5}{(10)}{ + 3y = -29}$ ${y = 7}$